@Article{CMR-33-2,
author = {Zhongjin, Chen and Zhao, Shuo},
title = {Two Bijections on Weighted Motzkin Paths},
journal = {Communications in Mathematical Research },
year = {2017},
volume = {33},
number = {2},
pages = {149--159},
abstract = {<p style="text-align: justify;">In this paper, we provide a bijection between the set of underdiagonal lattice paths of length $n$ and the set of (2,2)-Motzkin paths of length $n$. Besides, we generalize the bijection of Shapiro and Wang (Shapiro L W, Wang C J. A bijection between 3-Motzkin paths and Schröder paths with no peak at odd height. J. Integer Seq., 2009, 12: Article 09.3.2.) to a bijection between $k$-Motzkin paths and ($k$−2)-Schröder paths with no horizontal step at even height. It is interesting that the second bijection is a generalization of the well-known bijection between Dyck paths and 2-Motzkin paths.&nbsp;</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2017.02.07},
url = {https://global-sci.com/article/81643/two-bijections-on-weighted-motzkin-paths}
}